Caroline Wozniacki’s victory over Maria Sharapova Sunday at the 2014 U.S. Open capped off the madness of the women’s singles bracket at the U.S. Open. Only two of the top eight seeds—Serena Williams and Eugenie Bouchard—made it past the first week, with Bouchard falling Monday.
By comparison, the men’s side of the bracket has gone almost exactly according to form. Only one unseeded player—Austrian Dominic Thiem—made the second week and 11 of the top 16 seeds made it to the fourth round (to three and nine, respectively, in the women’s bracket).
On the women’s side this kind of disruption is hardly unusual—six of the top eight seeds lost before the quarters at Wimbledon in 2014. Consistency has likewise been the narrative of the men’s game, with three players (Roger Federer, Rafael Nadal, and Novak Djokovic) taking home 34 of the last 38 Slams.
To empirically test the hypothesis that the women’s draw is more volatile than the men’s, as well as try to quantify what have been the “craziest” Grand Slams of the modern era, I took each Grand Slam since 2001 (when the format switched from 16 to 32 seeds) and applied a simple algorithm to roughly measure how the results of each tournament differed from the bracket.
In each draw, I used the following table to assign a number to each seed. The number is based on the number of wins the seed had beyond what (s)he was expected to have. For example, the player seeded first is expected to win the tournament (seven matches in total). If the first seed loses in the fourth round, (s)he is assigned a score of -4 for underperforming by four wins. Conversely, a 32nd seed—expected to lose in the third round—who makes the finals would get a score of 4, having won four more matches than expected.
Using this methodology, I created two numbers for each tournament. The first (call it UVar, for unseeded variability), the absolute value of the sum of the results, calculates the number of unexpected matches won by unseeded players. The intuition behind this is that if all eight seeds make the quarterfinals (or if all 32 seeds make the third round), then the scores will all even out—i.e. one player’s overachievement will perfectly cancel out another player’s underachievement. UVar from that point forward will thus equal 0.
The second score (call it AVar, for absolute variability), taking the sum of the absolute value of the results, is more illustrative of how results vary from bracket projections. Take a four-team seeded tournament; no matter how the three matches are decided, the UVar will always be a 0. However, if the fourth seed beats the third seed in the final, it will have an AVar of 6, a better indication of how “crazy” the tournament was.
The following line chart shows the annual average AVar across the four Grand Slams for both the men’s and women’s draws over each of the last 14 years. The only Slams that are excluded are the current U.S. Open and the 2001 Australian and French Opens (the switch to 32 seeds was made that year at Wimbledon):
The graph shows an interesting trend. For one, the chaos in the women’s game that is so often trumpeted is a relatively short, four-year, trend. At the beginning of the century, the men’s game—stuck in the interlude between the peak of Pete Sampras and the ascent of Federer—was pure chaos. The calendar year of 2002 comprises four of the five craziest Slams since 2001. The aforementioned 2014 Wimbledon—the second craziest women’s Grand Slam—would have been the second most sane tournament that year.
The graph shows how over time the men’s game stabilized. The stability came from the top of the field—both Federer and Djokovic have run up consecutive semifinal streaks of 15 or higher over the course of their careers; by comparison’s sake, Serena’s longest semifinal streak spanned six tournaments. One of the top two seeds won the tournament 35 times on the men’s side, but just 21 times in the women’s draw.
The lowest seeded player to win a Grand Slam since 2007 was Stanislas Wawrinka, seeded eighth, in Australia. Over that same period, three different women seeded ninth and below (or unseeded) won Slams.
Beyond the absolute variance, we can see that UVar (graphed below) has generally followed the same trends as AVar.
Ultimately, we can use this method to find the craziest Grand Slams of the modern era. Both the craziest and sanest Grand Slams for both the men and women are shown below. The numbers reinforce what was already apparent—although the women’s tour has recently been wrecked by havoc, the craziest days of the men’s tour—at least for now—are behind them.